Lesnik, Karol

Abstract [en]

Comparison of level functions considered by Halperin and Sinnamon is discussed. Moreover, connections between Lorentz-type spaces, down spaces, Ces{\`a}ro spaces and Sawyer's duality formula are explained. Applying the ideas of Sinnamon, we prove the duality theorem for Orlicz-Lorentz spaces, which generalizes the recent result of Kami\'nska, Le\'snik and Raynaud (and Nakamura). Finally, some applications of level functions to geometry of Orlicz-Lorentz spaces are also presented.